1. **State the problem:** We have a set of temperatures recorded over two weeks: 56, 56, 58, 58, 60, 62, 62, 58, 56, 56, 55, 54, 55, 53.
2. **Organize the data:** Sort the data in ascending order:
$$53, 54, 55, 55, 56, 56, 56, 56, 58, 58, 58, 60, 62, 62$$
3. **Find the minimum and maximum values:**
- Minimum = 53
- Maximum = 62
4. **Find the median (Q2):**
Since there are 14 data points (even number), median is average of 7th and 8th values:
$$\frac{56 + 56}{2} = 56$$
5. **Find the first quartile (Q1):**
Q1 is median of first 7 values:
$$53, 54, 55, 55, 56, 56, 56$$
Median is 4th value = 55
6. **Find the third quartile (Q3):**
Q3 is median of last 7 values:
$$56, 58, 58, 58, 60, 62, 62$$
Median is 4th value = 58
7. **Summary:**
- Minimum = 53
- Q1 = 55
- Median = 56
- Q3 = 58
- Maximum = 62
8. **Interpretation:**
The box plot should have whiskers at 53 and 62, box from 55 to 58, and median line at 56.
9. **Compare with given box plots:**
The described box plot matches the one with whiskers at about 54 and 62, box from about 55 to 58, median about 56, except the minimum is 53, not 54.
Since the minimum is 53, the whisker should be at 53, not 54.
Therefore, the correct box plot is the one with whiskers at 53 and 62, box from 55 to 58, median at 56.
**Final answer:** The box plot with whiskers at 53 and 62, box from 55 to 58, and median at 56 represents the data.
Temperature Boxplot 3953Eb
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.